A threedimensional analysis of natural convection in a toroidal loop
Abstract
Flow through a toroidal loop oriented in a vertical plane is studied. This system is a simple example of a class of devices known as thermosyphons or natural circulation loops, which have many applications. When the toroidal loop is heated from below and cooled from above, an unstable density gradient is created in the fluid. Under the influence of gravity, the lighter fluid rises and the heavier fluid fails. Thus, the fluid flows due only to natural convection. Experiments on the toroidal thermosyphon have shown that under steady state flow conditions, the axial velocity and the temperature are nonaxisymmetric, the cross stream velocities are nonzero and regions of streamwise flow reversal exist. The simplified one and two dimensional analyses performed to date have not been able to predict these phenomena. The development of a finite difference computer program for performing a three dimensional analysis of the steady state fluid flow and heat transfer in the toroidal thermosyphon is described. Regions of streamwise flow reversal are predicted in some cases. Simplified analyses which do not take the flow reversals into account are shown to be substantially in error. Hence, the current analysis yields insight into the three dimensional aspects of the flow, which could not be predicted by earlier more simplified analyses.
 Publication:

Ph.D. Thesis
 Pub Date:
 June 1984
 Bibcode:
 1984PhDT........29L
 Keywords:

 Closed Cycles;
 Convective Flow;
 Convective Heat Transfer;
 Density Distribution;
 Equilibrium Flow;
 Friction Factor;
 Gradients;
 Loops;
 Reversed Flow;
 Steady State;
 Thermosiphons;
 Three Dimensional Flow;
 Toroids;
 Buoyancy;
 Computer Programs;
 Finite Difference Theory;
 Laminar Flow;
 Nusselt Number;
 Pipe Flow;
 Wall Flow;
 Fluid Mechanics and Heat Transfer